Hyperbolic Conservation Laws and the Compensated Compactness Method: 1st Edition (Hardback) book cover

Hyperbolic Conservation Laws and the Compensated Compactness Method

1st Edition

By Yunguang Lu

Chapman and Hall/CRC

256 pages | 10 B/W Illus.

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pub: 2002-09-27
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Description

The method of compensated compactness as a technique for studying hyperbolic conservation laws is of fundamental importance in many branches of applied mathematics. Until now, however, most accounts of this method have been confined to research papers. Offering the first comprehensive treatment, Hyperbolic Conservation Laws and the Compensated Compactness Method gathers together into a single volume the essential ideas and developments.

The authors begin with the fundamental theorems, then consider the Cauchy problem of the scalar equation, build a framework for L8 estimates of viscosity solutions, and introduce the Invariant Region Theory. The study then turns to methods for symmetric systems of two equations and two equations with quadratic flux, and the extension of these methods to the Le Roux system. After examining the system of polytropic gas dynamics (g-law), the authors first study two special systems of one-dimensional Euler equations, then consider the general Euler equations for one-dimensional compressible fluid flow, and extend that method to systems of elasticity in L8 space. Weak solutions for the elasticity system are introduced and an application to adiabatic gas flow through porous media is considered. The final four chapters explore applications of the compensated compactness method to the relaxation problem.

With its careful account of the underlying ideas, development of applications in key areas, an inclusion of the author's own contributions to the field, this monograph will prove a welcome addition to the literature and to your library.

Reviews

"The book is carefully written and will be appreciated both by PhD students and experts in the field as one of a few books gathering the knowledge … [previously] dispersed among research papers."

- EMS Newsletter, Dec. 2004

Table of Contents

PRELIMINARY

THEORY OF COMPENSATED COMPACTNESS

SCALAR EQUATION

ELEMENTARY IN HYPERBOLIC SYSTEM

A SYMMETRY SYSTEM

A SYSTEM OF QUADRATIC FLUX

LE ROUX SYSTEM

SYSTEM OF POLYTROPIC GAS DYNAMICS

TWO SYSTEMS OF EULER-EQUATIONS

GENERAL SYSTEM OF EULER-EQUATIONS

EXTENDED SYSTEMS OF ELASTICITY

L[p] CASE FOR SYSTEMS OF ELASTICITY

ELEMENTARY IN RELAXATION

RELAXATION WITH DIFFUSION

SYSTEMS WITH STIFF RELAXATION

RELAXATION FOR 3 x 3 SYSTEMS

BIBLIOGRAPHY

About the Author/Editors

Yunguang Lu is a Professor of Mathematics at the University of Columbia, Bogota and at the University of Science and Technology of China, Hefei.

About the Series

Monographs and Surveys in Pure and Applied Mathematics

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
MAT003000
MATHEMATICS / Applied
MAT007000
MATHEMATICS / Differential Equations
SCI040000
SCIENCE / Mathematical Physics